Parameterized Analysis of 2-DOF Motion Platform Based on ADAMS

According to the functions of parametric modeling and analysis from ADAMS, this thesis was established a parametric simulation model in order to optimize the rated output power of electric cylinders according to the real field environment. First, the variable which could affect sensitivity of the output variables was chosen by the electric cylinder's elongation which was obtained through loop vector method. Then this thesis tried to get the optimum optimization design parameters through the simulation, and the change of rated output power affected by the change of parameters, meanwhile, made a filter and calibration of parameters which have greater influence on sensibilities. The goal of design could meet the qualification with less work load and faster speed. It is concluded that the change of the location parameters affects the rated output power. Keyword: 2-DOF motion platform; ADAMS; parameterized analysis; simulation DOI: 10.1051/ C © Owned by the authors, published by EDP Sciences, 2015 / 030 ( 2015) 201 conf Web of Conferences , 5 MATEC 22 22030 atec m 0 0 This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 6 6 Article available at http://www.matec-conferences.org or http://dx.doi.org/10.1051/matecconf/20152203006 2 INTRODUCTION OF 2-DOF MOTION PLATFORM'S STRUCTURE As shown in Figure 1, the 2-DOF motion platform consists of moving platform, middle supporting platform, static platform, servo electric cylinder, hinges and so on. The servo electric cylinder as A,B shows parallel with the central axis O0O1O2O3 of platform and it was vertical to servo electric cylinder C; the moving platform was connected with static platform by middle platform; cylinders were connected with moving and static platform by hinges; platform moves through the servo electric cylinders. Stabilized the optical terminal on the moving platform; it simulated attitude change on board by controlling three electric cylinders' telescopic motion of the azimuth and elevation. The moving platform and middle supporting platform were connected by structure of frames. This scheme not only increases space to install equipment, but decreases the height of equipment's center of gravity to improve the equipment stability as well. It cuts the size of the motion platform then lightens the weight of the whole platform on the premise which meets the demand of enough stiffness. Because of the motion platform moved by the way supported by middle and moved by two electric cylinders and maintenance-free bearing in the middle support nearly most loads, therefore, it reduces the demand for electric cylinder's output torque. Furthermore, it meets the low power requirements which chosen in field environment test. 3 PARAMETERIZED MODELING OF MOTION PLARFORM 3.1 Selection of the design variables Simplify the motion platform for the convenience of parameterized modeling as shown in Figure 2, the selection of the design variables affected the performance of the prototype , which was the main content for parametric design, and it had great influence on the motion platform. The variable which could affect sensitivity of the output variables was chosen by the electric cylinder's elongation which was got through the loop vector method. Based on the analysis of motion platform, the model of electric cylinder was parted from the motion platform as shown in Figure 3. Coordinate system O0-X0Y0Z0 was established. Three key points in the coordinate system were O0 ( 0, 0, 0 ), B1( R0, 0, 0 ), O1( 0, 0,q ). R0 was the radius of flexural pivot on static platform and q was vertical distance between the rotation center of middle support's hinge and static platform. R0 and q are constant. The point B2's coordinate was (r0cosλ2, 0, r0sinλ2) in moving coordinate system O1-X1Y1Z1 based on an initial state. r0 is a linear distance between flexural pivot B2 and hinge O1. λ2 was angle between and +X1. According to the principle of coordinate changed, the position vector in moving coordinate system could be transformed to position vector in static coordinate system through the transform formula, which was shown as follows: P=T P'+P0 2 1B O


INTRODUCTION
Nowadays, the parametric design was an emphasis in the study of CAD [1] .The MSC ADAMS possesses the functions of parametric modeling and analyzing in order to improve the efficiency of mechanism design and shorten the designing period.The document [2] regarded the minimum driving angles as an optimization goal, and the lengths of links are parameterized via ADAMS by creating design parameters.The document [3] regarded the minimum base driving torque as an optimization goal to get the optimal solution of substructure driving torque.The document [4] chose side way displacement as an optimization goal to finish parametric optimization.
The motion platform was used to be tested in field environment.It required that the rated output power of the electric cylinder should be as low as better, so it could meet the movement's demand which was due to power constrains in the field.So that it could reduce the requirement of power supply.Also, we should research the structure of motion platform deeper because every parameters of platform have different effects on the electric cylinder power.The location parameter as a very important design factor in the design process determined the motion platform's characteristics.So it was necessary to study on the relationship between motion platform and characteristics.The traditional method of analysis to the model which had modified until meeting the desired model and results was a mindless and repetitive task.And the method used in this paper was the first parametric model which was established by the modeling, analysis simulation and post processing module; and the rated output power of electric cylinder was lower by the above analysis and on the premise of meeting the practice; then we obtained the expected result which could reduce the requirement of power.ABSTRACT: According to the functions of parametric modeling and analysis from ADAMS, this thesis was established a parametric simulation model in order to optimize the rated output power of electric cylinders according to the real field environment.First, the variable which could affect sensitivity of the output variables was chosen by the electric cylinder's elongation which was obtained through loop vector method.Then this thesis tried to get the optimum optimization design parameters through the simulation, and the change of rated output power affected by the change of parameters, meanwhile, made a filter and calibration of parameters which have greater influence on sensibilities.The goal of design could meet the qualification with less work load and faster speed.It is concluded that the change of the location parameters affects the rated output power.Stabilized the optical terminal on the moving platform; it simulated attitude change on board by controlling three electric cylinders' telescopic motion of the azimuth and elevation.The moving platform and middle supporting platform were connected by structure of frames.This scheme not only increases space to install equipment, but decreases the height of equipment's center of gravity to improve the equipment stability as well.It cuts the size of the motion platform then lightens the weight of the whole platform on the premise which meets the demand of enough stiffness.Because of the motion platform moved by the way supported by middle and moved by two electric cylinders and maintenance-free bearing in the middle support nearly most loads, therefore, it reduces the demand for electric cylinder's output torque.Furthermore, it meets the low power requirements which chosen in field environment test.

PARAMETERIZED MODELING OF MOTION PLARFORM 3.1 Selection of the design variables
Simplify the motion platform for the convenience of parameterized modeling as shown in Figure 2, the selection of the design variables affected the performance of the prototype [5][6] , which was the main content for parametric design, and it had great influence on the motion platform.The variable which could affect sensitivity of the output variables was chosen by the electric cylinder's elongation which was got through the loop vector method.
Based on the analysis of motion platform, the model of electric cylinder was parted from the motion platform as shown in Figure 3.
Coordinate system O 0 -X 0 Y 0 Z 0 was established.Three key points in the coordinate system were O 0 ( 0, 0, 0 ), B 1 ( R 0 , 0, 0 ), O 1 ( 0, 0,q ).R 0 was the radius of flexural pivot on static platform and q was vertical distance between the rotation center of middle support's hinge and static platform.R0 and q are constant.
The point B 2 's coordinate was (r 0 cosλ 2 , 0, r 0 sinλ 2 ) in moving coordinate system O 1 -X 1 Y 1 Z 1 based on an initial state.r0 is a linear distance between flexural pivot B 2 and hinge O 1 .λ 2 was angle between and +X 1 .
According to the principle of coordinate changed, the position vector in moving coordinate system could be transformed to position vector in static coordinate system through the transform formula, which was shown as follows: P=T P'+P 0   = ; Relational expression of electric cylinder C's elongation is obtained as the same as that mentioned earlier.We had solved the expression which is up to the rod length in linear regression way.Furthermore, we evaluated the differential divisor variable between input and output by the LINGO software.
The variable which could affect sensitivity of the output variables must be chosen for parametric modeling of motion platform.So eight key points were chosen in this paper, which were the center point O1 of moving platform, the center point O2 of moving platform, and the end points A 1 , A 2 , B 1 , B 2 , C 1 , and C 2 on the three electric cylinders.This points were reference points, which corresponded to eight design variables, named DV_1~DV_8.

Established the parametric model of motion platform
The simplified model was established by modeling tool in ADAMS, which could make parametric design for the motion platform.In the process of modeling, the point could be moved to change the layout of electric cylinder through location parameter of the motion platform by establishing the point.Figure 4 showed the model according to the point coordinates:   The study about sensitivity of structure's parameters was mainly about the influenced degree of sensitivity of single design variable on the overall prototype.The design variables were analyzed in the set range, which had effects on sensibilities to output power.Making a filtering and revising of parameters which have greater influence on sensibilities could shorten the computation time and save the development cost.It regarded the electric cylinder's power dissipation as an object function, meanwhile, it regarded structure's parameters as design variable, furthermore, it would evaluate by the index of sensitivity.
In type: O desired value  First of all, the number of iteration times was 5. Then we set the maximum power consumption of electric cylinder as the target and design parameter values as DV_1: Figure 5 to Figure 8 depicted that the research about the influence law of platform to power of electric cylinder B,C and law of each size's sensitivity as following variable DV_1's change.It could be used to calculate that the sensitivity of variable DV_1 to electric cylinder C was 0.83, and that one to electric cylinder C was 1.53 in the initial position.The larger sensitivity is, the greater design variable influences of output power of the electric cylinder are.Therefore, the change of the electric cylinder B must be considered before changing the value of DV_1.Similarly, sensitivity of the electric cylinder affected by 8 parameters was got through the simulation, and the results are shown in Table 3: According to the analysis of the key parameters in Table 3, the result could be obtained that DV_1, DV_5 and DV_6 had great influence on the simulation platform of the overall power consumption.Therefore, three design variables were chosen to analyze again as the final optimization variables could be used to keep the platform optimizing.The installation position of electric cylinder C had great influence on output power, so it was a main factor in the design.Others weren't treated as optimization design variables which sensitivity is smaller and had little effects on output power.Figure 9 showed the iterative optimization process curve, and the optimization results were: DV_1=240.12;DV_5=136.74;DV_6=100.46;the power consumption was the lowest.Then we could determine the electric cylinder's position.

Keyword: 2 -
DOF motion platform; ADAMS; parameterized analysis; simulation DOI: 10.1051/ C Owned by the authors, published by EDP Sciences, 2015 2-DOF MOTION PLAT-FORM'S STRUCTURE As shown in Figure 1, the 2-DOF motion platform consists of moving platform, middle supporting platform, static platform, servo electric cylinder, hinges and so on.The servo electric cylinder as A,B shows parallel with the central axis O0O1O2O3 of platform and it was vertical to servo electric cylinder C; the moving platform was connected with static platform by middle platform; cylinders were connected with moving and static platform by hinges; platform moves through the servo electric cylinders.

Figure 3 .
Figure 3. Model of electric cylinder elongation of electric cylinder B is shown as follows: Insert the coordinate of B1 into L B :

1
Research about the sensitivity of structure parameter

Figure 5 .Figure 6 .
Figure 5. Influence law of variable DV_1 to the power of electric cylinder B paper mainly evaluated the electric cylinder B and C due to the servo electric cylinder A was a supplementary role in the movement and stressed less than the other two electric cylinders.It took X-coordinate of hinge A 1 variables DV_1 as an exam-ple to introduce the calculation about sensitivity of the single design variable.

Figure 7 .Figure 8 .Figure 9 .
Figure 7. Influence law of variable DV_1 to the power of electric cylinder C

4. 2
Optimizing structure parameters of the platform Due to the structure parameters, the servo electric cylinder C was more sensitive than electric cylinder B. Then the following was regarded the minimum power of electric cylinder B as the optimization objective function by iterative optimization design.According to the trend of variable sensitivity, the definition change interval was that DV_1 was [-245, -235]; DV_5 was [130, 142]; DV_6 was [95, 105].

Table 1 .
Coordinates of reference points

Table 2 .
Coordinate of design variable's starting value

Table 3 .
Sensitivity of electric cylinder C about design variable